The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the spectrum of thermal radiation of scalar particles by Kerr (and Schwarzschild) black holes can be explicitly derived on the basis of a 2-dimensional conformal symmetry arising in the wave equation near the horizon. This result reinforces the recently conjectured relation between Kerr geometry and a 2-dimensional conformal field theory.